For Congress, it is the legislative equivalent of time travel: a kind of law that allows lawmakers to reach into the future, and force decisions on the Congresses yet to come.

On Tuesday, the GOP-led House will vote on such a measure, part of a broader plan to reduce the deficit that has been nicknamed “cut, cap and balance.” For the next 10 years, the bill would set caps on the money available for later lawmakers to spend.

But, as with all stories about time travel, there’s a catch. In Congress, giving orders to the future rarely works; lawmakers simply ignore or repeal them.

So why would the current plan to “cap” spending work?

It turns out that even supporters have their doubts that it would.

“They have tried doing all these things in the past, but what future Congresses do is, they ignore it,” said Rep. Raul R. Labrador (R), a freshman legislator from Idaho.

But he still supports implementing a cap. The idea is that legal caps might restrain Congress for a few years, while a balanced budget amendment (the “balance” part of the pledge) is ratified by the states. “It’s the amendment that’s going to make future Congresses be held to” spending limits, Labrador said.

The “cut, cap, balance” plan has emerged as a key demand of House Republicans, with just 14 days remaining before the Aug. 2 deadline to raise the national debt ceiling. House GOP leaders vowed to press ahead with the vote, despite President Obama’s threat to veto the measure if it passed.

The bill would not allow an increase in the ceiling until three conditions were met:

First, the bill would require a reduction of $111 billion in federal spending in fiscal 2012, exempting defense, Medicare and Social Security from cuts. Then, it would set caps on future spending, limiting it to a certain percentage of the gross domestic product. If the rule is violated, the bill would require sharp, automatic, spending cuts.

Third, the bill would require both houses of Congress to pass a balanced budget amendment.

“No one wants to default on our debt,” Majority Leader Eric Cantor (R-Va.) said in a statement Monday. “That is why House Republicans are bringing forth this plan . . . with the necessary safeguards to make sure that we don’t continue to kick the can down the road.”

This demand signals that, despite its promises to upend Washington’s business as usual, the GOP-led House has something in common with many lawmakers who came before them.

They believe they are the exception to a dismal tradition: more responsible than the lawmakers who will come after them, and qualified to tell those guys what to do.

“It’s difficult to make a credible argument that we can or should simply trust Congress to do the right thing,” said Sen. Mike Lee (R-Utah). That’s the intent behind the “cap” and “balance” elements of the pledge: “you need something to guide Congress” in the future, he said.

For some in Washington, the “cap” part of this effort sounds like a repeat of history.

“This is like ‘Groundhog Day’,” said Steve Bell, a former Republican Senate staffer who now works at the Bipartisan Policy Center, referring to the 1993 movie in which Bill Murray’s character is forced to repeatedly re-live the same dismal day. “We tried that 25 years ago. It didn’t work.”

Bell was involved, as a staffer, in one of the earliest attempts to set spending rules for future Congresses, imposed after a debt showdown in 1985. A bill, named Gramm-Rudman-Hollings after its Senate patrons, required future Congresses to limit the deficits they ran. If not, the bill required automatic cuts in spending.

But the law did not have the desired impact. Later Congresses found ways around it, and it was effectively terminated in 1990.

In the 1990s, Congress imposed a new rule, requiring lawmakers to balance new spending on “entitlement” programs with either new cuts or new taxes. The “pay as you go” rule actually seemed to change spending habits for several years, experts say.

But then Congress again began finding ways to evade orders from the past. In many cases, it designated huge amounts of money as “emergency” spending, which didn’t count.

In interviews, several supporters of the “cut, cap, balance” bill acknowledged that the same fate might befall their legal “cap.” They said that only a balanced-budget amendment, permanently written into the Constitution, could really restrain the legislators of tomorrow.

But such an amendment is not a sure thing. The Democratic-led Senate seems unlikely to approve it. And even then, ratification would require the approval of 38 states.

If an amendment is never ratified, would legal caps still make a difference? Sen. Patrick J. Toomey (R-Pa.) said he thought they would, since lawmakers might be reluctant to flout them in later years.

If the future can’t be controlled, that logic says, it can at least be embarrassed.

“It raises the hurdle. It makes it tougher for a future Congress to spend more,” Toomey said. “It doesn’t make it impossible.”